A model is developed to describe odd-parity baryon resonances generated dynamically through a unitary baryon-meson coupled-channels approach. The scheme applies to channels with light- and/or heavy-quark content. Distinct features of the model are that i) the interaction is an S-wave contact one, ii) it reduces to the SU(3) Weinberg-Tomozawa Hamiltonian when light pseudoscalar mesons are involved, thus respecting chiral symmetry, iii) spin-flavor is preserved in the light-quark sector, and iv) heavy-quark spin symmetry is fulfilled in the heavy-quark sector. In particular, baryon-meson states with different content in c or in (c) over bar do not mix. The model is a minimal one and it contains no free parameters. In this work, we focus on baryon resonances with hidden charm (at least one (c) over bar and one c quark). We analyze several possible sectors and, for the sector with zero net charm, we write down the most general Lagrangian consistent with SU(3) and heavy-quark spin symmetry. We explicitly study the N and Delta states, which are produced from the S-wave interaction of pseudoscalar and vector mesons with 1/2(+) and 3/2(+) baryons within the charmless and strangeless hidden-charm sector. We predict seven odd-parity N-like and five Delta-like states with masses around 4 GeV, most of them as bound states. These states form heavy-quark spin multiplets, which are almost degenerate in mass. The predicted new resonances definitely cannot be accommodated by quark models with three constituent quarks and they might be looked for in the forthcoming PANDA experiment at the future FAIR facility.